Linear Programming Relaxations and Belief Propagation - An Empirical Study

The problem of finding the most probable (MAP) configuration in graphical models comes up in a wide range of applications. In a general graphical model this problem is NP hard, but various approximate algorithms have been developed. Linear programming (LP) relaxations are a standard method in computer science for approximating combinatorial problems and have been used for finding the most probable assignment in small graphical models. However, applying this powerful method to real-world problems is extremely challenging due to the large numbers of variables and constraints in the linear program. Tree-Reweighted Belief Propagation is a promising recent algorithm for solving LP relaxations, but little is known about its running time on large problems. In this paper we compare tree-reweighted belief propagation (TRBP) and powerful generalpurpose LP solvers (CPLEX) on relaxations of real-world graphical models from the fields of computer vision and computational biology. We find that TRBP...

• Type: Journal
• Year: 2006
• Where: JMLR
• Authors: Chen Yanover, Talya Meltzer, Yair Weiss
• Keywords: Belief Propagation, Graphical Models, JMLR 2006, Problems